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The population of a town in 2010 was 8,500 people. The population has decreased by 4.5% each year since. 

1. Write an equation showing how to find the population of the town years after 2010.

 

2. In what year will the population of the town equal 7,000 people? Show your calculations.

 

Thank you!

Guest May 21, 2018
 #1
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(a) 8,500-4.5%(t)

 

(b) 2010: 8,500

2011: 8117

2012: 7752

2013: 7403

2014: 7069

2015: 6751

Thus, it'll be \(\boxed{2015}\) , when the population will equal 7000.

smileysmiley

tertre  May 21, 2018
 #2
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Present population =PP

Future population =FP

 

FP = PP x [1 - 0.045]^t

7,000 = 8,500 x [0.955]^t        divide both sides by 8,500

0.823529... = 0.955^t              take the log of both sides

t =Log(0.823529) / Log(0.955)

t = 4.22 = ~ 4.25 years after 2010 when the population of the town will be about 7,000.

Guest May 21, 2018
edited by Guest  May 21, 2018

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